Problem: Solve for $q$, $ -\dfrac{10}{9q + 15} = -\dfrac{q + 5}{12q + 20} - \dfrac{8}{3q + 5} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $9q + 15$ $12q + 20$ and $3q + 5$ The common denominator is $36q + 60$ To get $36q + 60$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ -\dfrac{10}{9q + 15} \times \dfrac{4}{4} = -\dfrac{40}{36q + 60} $ To get $36q + 60$ in the denominator of the second term, multiply it by $\frac{3}{3}$ $ -\dfrac{q + 5}{12q + 20} \times \dfrac{3}{3} = -\dfrac{3q + 15}{36q + 60} $ To get $36q + 60$ in the denominator of the third term, multiply it by $\frac{12}{12}$ $ -\dfrac{8}{3q + 5} \times \dfrac{12}{12} = -\dfrac{96}{36q + 60} $ This give us: $ -\dfrac{40}{36q + 60} = -\dfrac{3q + 15}{36q + 60} - \dfrac{96}{36q + 60} $ If we multiply both sides of the equation by $36q + 60$ , we get: $ -40 = -3q - 15 - 96$ $ -40 = -3q - 111$ $ 71 = -3q $ $ q = -\dfrac{71}{3}$